Method and device for establishing statistical constitutive model of damage of high-crustal-stress pore-containing rock

Abstract

The invention discloses a method for establishing a damage statistical constitutive model of a high-ground-stress pore-containing rock, and belongs to the technical field of rock constitutive relation basic research of deep underground engineering. The method comprises the following steps: on the basis of a rock damage statistical theory, introducing a porosity concept to quantitatively process the influence of pore volume change when the pore-containing rock is pressed, and constructing a corresponding pore-containing rock damage model; on the basis, an M-C nonlinear strength criterion and an H-B nonlinear strength criterion are used for constructing a rock infinitesimal strength measurement method capable of reflecting the nonlinear deformation characteristic of the pore-containing rock in the high ground stress compression state, and accordingly a damage statistical constitutive model suitable for the high ground stress pore-containing rock is established; and further carrying out sensitivity analysis of model parameters around the constitutive model. The method can accurately simulate the nonlinear deformation process of the pore-containing rock under the action of the deeply-buried high confining pressure, and can be applied to the technical field of basic research of a rock constitutive model of deeply-buried underground engineering.

Description

Technical Field

[0001] This invention belongs to the technical field of basic research on rock constitutive relations in deep underground engineering, specifically involving a method and device for establishing a statistical constitutive model of damage in porous rocks under high ground stress. Background Technology

[0002] In deep underground engineering, the deformation of rock engineering structures is a key indicator for stability control, and calculation and analysis of this deformation have always been an essential part of the design of such engineering structures.

[0003] As is well known, the deformation of rock engineering structures is closely related to the stress-strain relationship of the rock medium itself, i.e., the rock constitutive model. Since most rock media in actual engineering are not idealized materials, they contain numerous pores due to the influence of various natural factors. Pores refer to aggregates of defects, cracks, etc., within the rock. The presence of pores causes rocks to exhibit significant volumetric compressibility under pressure. Therefore, porosity is a ubiquitous factor in natural rocks and has a significant impact on rock constitutive relations; correspondingly, it is necessary to consider porosity as a core factor when establishing constitutive models for rocks containing porosity.

[0004] On the other hand, rocks buried deep underground are usually in a high-stress environment characterized by high confining pressure. Engineering practice shows that the deformation of rocks in this environment exhibits strong nonlinear characteristics. However, current research on statistical constitutive models for rock damage is mainly based on low confining pressure strength criteria, which makes it difficult for such constitutive models to effectively simulate the nonlinear deformation characteristics of rocks under high stress with high confining pressure as an important feature.

[0005] Therefore, it is of great significance to carry out research on statistical constitutive models of damage to porous rocks under high ground stress in order to more accurately describe and predict the nonlinear deformation characteristics of porous rocks in deeply buried underground engineering. Summary of the Invention

[0006] The purpose of this invention is to provide a method and apparatus for establishing a statistical constitutive model of damage in porous rocks under high ground stress, which can solve at least one technical problem mentioned in the background art.

[0007] To solve the above-mentioned technical problems, the present invention is implemented as follows: A method for establishing a statistical constitutive model for damage in porous rocks under high geostress includes the following steps: Step S1: Introduce the concept of porosity and quantify the influence of pores on the volume change of porous rocks under pressure. Step S2: Using the MC nonlinear strength criterion and the HB nonlinear strength criterion, construct a rock nonlinear strength criterion considering high ground stress, and establish a rock micro-element strength measurement method that can reflect the nonlinear deformation characteristics of porous rocks. Step S3: Establish a damage statistical constitutive model to simulate the nonlinear deformation process of porous rocks under high ground stress, and propose a method for calculating the model parameters corresponding to this constitutive model. Step S4: Plot the theoretical curves based on the MC nonlinear strength criterion and the HB nonlinear strength criterion, and compare and analyze them with the corresponding experimental data curves to verify the effectiveness and rationality of the statistical constitutive model for damage to porous rocks under high ground stress. Step S5: Considering the variation in initial porosity, conduct a sensitivity analysis of the statistical constitutive model for damage in porous rocks under high ground stress, focusing on the influence of different initial porosities on the theoretical curve.

[0008] Compared with the prior art, the advantages of this invention are as follows: 1. This invention introduces porosity as a quantitative index to characterize the influence of volume changes in porous rocks, thereby constructing a new damage model for porous rocks. This provides a new approach for the study of rock constitutive relations in deep underground engineering and further expands the application scope of statistical constitutive relations of rock damage.

[0009] 2. This invention utilizes the MC nonlinear strength criterion and the HB nonlinear strength criterion to construct a micro-element strength measurement method that can reflect the nonlinear deformation characteristics of rocks under high ground stress. It establishes a damage statistical constitutive model for simulating the nonlinear deformation process of porous rocks under high ground stress and a method for determining the model parameters. Through comparative analysis of model curves and experimental curves, the effectiveness and rationality of the damage statistical constitutive model for porous rocks under high ground stress are verified.

[0010] 3. The method provided by this invention has simple steps, fully considers the actual needs of engineering, and effectively makes up for the fact that the model curves of existing technologies cannot effectively simulate the nonlinear deformation characteristics of porous rocks under deep-buried high-stress environments. Therefore, it has a wide range of applications and broad prospects, and is of great significance for the research on simulation methods of rock deformation processes in deep-buried underground engineering structures. Attached Figure Description

[0011] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort, wherein: Figure 1A flowchart illustrating a method for establishing a statistical constitutive model for damage in porous rocks under high ground stress, as provided in an embodiment of the present invention; Figure 2 Yield parameters of the MC nonlinear strength criterion provided in embodiments of the present invention , The fitting relationship diagram; Figure 3 Peak parameters of the MC nonlinear intensity criterion provided in the embodiments of the present invention , The fitting relationship diagram; Figure 4 Yield parameters of the HB nonlinear strength criterion provided in embodiments of the present invention , The fitting relationship diagram; Figure 5 Peak parameters of the HB nonlinear intensity criterion provided in the embodiments of the present invention , The fitting relationship diagram; Figure 6 A graph showing the relationship between peak strain and confining pressure in rock provided in an embodiment of the present invention; Figure 7 The confining pressure provided in the embodiments of the present invention Comparison of theoretical and experimental curves of MC nonlinear strength criterion at 10 MPa; Figure 8 The confining pressure provided in the embodiments of the present invention Comparison of theoretical and experimental curves of MC nonlinear strength criterion at 20 MPa; Figure 9 The confining pressure provided in the embodiments of the present invention Comparison of theoretical and experimental curves of MC nonlinear strength criterion at 40 MPa; Figure 10 The confining pressure provided in the embodiments of the present invention Comparison of theoretical and experimental curves of MC nonlinear strength criterion at 60 MPa; Figure 11 The confining pressure provided in the embodiments of the present invention Comparison of theoretical and experimental curves of MC nonlinear strength criterion at 70 MPa; Figure 12 The confining pressure provided in the embodiments of the present invention Comparison of theoretical and experimental curves of HB nonlinear strength criterion at 10 MPa; Figure 13 The confining pressure provided in the embodiments of the present invention Comparison of theoretical and experimental curves of HB nonlinear strength criterion at 20 MPa; Figure 14 The confining pressure provided in the embodiments of the present invention Comparison of theoretical and experimental curves of HB nonlinear strength criterion at 40 MPa; Figure 15 The confining pressure provided in the embodiments of the present invention Comparison of theoretical and experimental curves of HB nonlinear strength criterion at 60 MPa; Figure 16 The confining pressure provided in the embodiments of the present invention Comparison of theoretical and experimental curves of HB nonlinear strength criterion at 70 MPa; Figure 17 The confining pressure provided in the embodiments of the present invention Comparison of theoretical and experimental curves of the MC nonlinear strength criterion at 10 MPa; Figure 18 The confining pressure provided in the embodiments of the present invention Theoretical curves of the MC nonlinear strength criterion and experimental curves of the HB nonlinear strength criterion at 20 MPa; Figure 19 The confining pressure provided in the embodiments of the present invention Comparison of theoretical and experimental curves of the MC nonlinear strength criterion at 40 MPa; Figure 20 The confining pressure provided in the embodiments of the present invention Comparison of theoretical and experimental curves of the MC nonlinear strength criterion at 60 MPa; Figure 21 The confining pressure provided in the embodiments of the present invention Theoretical curves of the MC nonlinear strength criterion and experimental curves of the HB nonlinear strength criterion at 70 MPa; Figure 22 The theoretical and experimental curves are shown in the embodiment of the present invention when the initial porosity is 0%, 3%, 6%, 9%, and 12%. Detailed Implementation

[0012] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0013] Please see Figure 1 As shown, this embodiment of the invention provides a method for establishing a statistical constitutive model of damage in porous rocks under high geostress, comprising the following steps: Step S1: Introduce the concept of porosity and quantify the influence of pores on the volume change of porous rocks under pressure. Step S2: Using the MC nonlinear strength criterion and the HB nonlinear strength criterion, construct a rock nonlinear strength criterion considering high ground stress, and establish a rock micro-element strength measurement method that can reflect the nonlinear deformation characteristics of porous rocks. Step S3: Establish a damage statistical constitutive model to simulate the nonlinear deformation process of porous rocks under high ground stress, and propose a method for calculating the model parameters corresponding to this constitutive model. Step S4: Plot the theoretical curves based on the MC nonlinear strength criterion and the HB nonlinear strength criterion, and compare and analyze them with the corresponding experimental data curves to verify the effectiveness and rationality of the statistical constitutive model for damage to porous rocks under high ground stress. Step S5: Considering the variation in initial porosity, conduct a sensitivity analysis of the statistical constitutive model for damage in porous rocks under high ground stress, focusing on the influence of different initial porosities on the theoretical curve.

[0014] In step S1, the concept of porosity is introduced to quantify the impact of porosity changes on rock volume changes under pressure, specifically including: The porous rock mass is considered as three units: porous unit, damaged unit and undamaged unit; The stress on porous rocks is defined as apparent stress. The corresponding effective area is The effective areas of the damaged unit, the undamaged unit, and the porous unit are respectively... , , Then we have: (1) The stress experienced by an undamaged element is defined as the effective stress. Now, assuming only the undamaged elements are subjected to force, the stress on the entire rock and the stress on the undamaged elements have the following relationship: (2) Let the porosity of the rock be... According to the proportional relationship, we have: (3) The proportion of rock-damaged units is defined as the damage factor. According to the proportional relationship, we have: (4) Combined equations (1) Equation (4) yields a damage model characterizing porous rocks, expressed as follows: (5) Assuming the undamaged rock unit follows the generalized Hookean rule Then we have: (6) In the formula, and and The mechanical meanings of these two terms are the same, both representing effective stress. Deformation mode of undamaged units in rock ; Poisson's finite element in the rock ; This represents the microscopic strain of undamaged units within the rock. During rock deformation, there is a relationship of deformation coordination among the various rock elements. ,but: (7) In the formula, Indicates the apparent strain of the rock; Based on the above deformation compatibility relationships, then: (8) In the formula, Poisson's ratio for the entire rock; Combined equations (6) Equation (8) gives the effective stress as: (9) Substituting equation (9) into equation (5), we obtain the expression for apparent stress: (10) During the deformation process of porous rocks, the porosity changes continuously with the volume of the rock. Therefore, let the initial porosity of the rock be... Now, we take a tiny unit from the rock as the object of study, and denote its length as... , width is Gao Wei Assume that during the loading process, due to changes in pore volume, the length, width, and height of the representative element undergo compressive deformation, respectively. If we assume that the volume of the solid portion of the rock remains constant before and after deformation, then we can establish the following equation: (11) Furthermore, due to strain Then equation (11) becomes: (12) Rearranging equation (12) yields: (13) Since the strains are all small micro-quantities, cancel the right side of equation (13) , , and We can obtain: (14) For ease of writing, the following is hereby ordered: (15) Substituting equation (15) into equation (14) yields the porosity: (16) From equation (9), we can obtain: (17) (18) (19) From equation (5), we can obtain: (20) (twenty one) Combined equations (17) From equation (29), we can obtain: (twenty two) (twenty three) Substituting equations (22) and (23) into equation (15) and then into equation (16), we get: (twenty four).

[0015] In step S2, it is assumed that the strength of the rock element follows the Weibull distribution. Considering the influence of threshold damage, the following rock damage evolution model can be obtained: (25) In the formula, The strength of a rock micro-element; These are model parameters; Accordingly, the statistical constitutive model of damage in porous rocks can be expressed as: (26).

[0016] In step S2, taking the MC nonlinear criterion as an example, its corresponding intensity envelope function expression is: (27) In the formula, a and b are the calculation parameters corresponding to the function expression; Considering the geometric properties of the MC nonlinear criterion, we can obtain: (28) (29) Combined equations (28) Equation (29) gives: (30) From equation (27), we can obtain: (31) Substituting equation (31) into equation (30), we get: (32) By combining equations (27) and (32), we can obtain: (33) or: (34) Based on this combined with equation (28), we can obtain: (35) Therefore, for undamaged units in the rock, we have: (36) In the formula, , These are the calculation constants for the yield stress state; Accordingly, a method for measuring the intensity of infinitesimal elements can be established, namely: (37) Note that from equation (5), we can obtain: (38) (39) From equation (10), we can obtain: (40) Combined (37) Equation (40) gives the expression for the rock micro-element strength function based on the MC nonlinear strength criterion: (41).

[0017] In step S2, based on the fundamental principle of the HB nonlinear strength criterion, the stress expression can be obtained: (42) In the formula, It is the uniaxial compressive strength of rock k and s are empirical parameters; For undamaged units in the rock, we can obtain: (43) Accordingly, a method for measuring the strength of rock micro-elements can be established, namely: (44) Combined (38) Equations (40) and (44) give the expression for the rock micro-element strength function based on the HB nonlinear strength criterion: (45).

[0018] In step S3, when a complete, dense rock without obvious defects is taken and no confining pressure is applied, the rock micro-element strength is... Therefore, damage variable Taking 0, meaning the rock is not damaged at this point; based on the case where the damage variable D is 0, assuming the porous rock is subjected to a load P, and assuming the initial porosity is... If the area subjected to the force is S, then: (46) (47) By combining (46) and (47), the elastic modulus of the undamaged element can be obtained. Overall elastic modulus of rock Quantitative relationship between them: (48) When the obtained rock is similar to that in the actual natural environment and has obvious defects, the proportion of pore units will be relatively large, and the influence of pore units cannot be ignored. In this case, a uniaxial compression test is performed, and the initially measured elastic modulus value is... Then, using the above-mentioned experimental results, The initial porosity can be obtained from the value of , according to equation (48). : (49) According to conventional triaxial tests, the initial state of the rock sample is under hydrostatic pressure. At this point, an initial axial strain is generated. The curve obtained from the experiment is a deviatoric stress curve. With axial strain The relationship curve; under hydrostatic pressure, the initial strain can be obtained by combining equations (10) and (24). : (50) Now assume that the coordinates of the peak point of the conventional triaxial test curve for porous rocks are... We can obtain: (51) In the formula, Represents the differential symbol; From equation (10), we can obtain: (52) According to equation (24), we can obtain: (53) Introduction , , As a substitute variable, we have: (54) (55) (56) Based on equations (54), (55), and (56), equation (53) can be transformed into the following expression: (57) By combining equations (51), (52), (54), and (57), we can obtain: (58) On both sides of equation (56) Taking the derivative, we get: (59) Taking the logarithm of both sides of equation (55) yields: (60) Then, adjust both sides of equation (60) Taking the derivative, we get: (61) Combining equation (55) and equation (61), we get: (62) From equation (25), we can obtain: (63) On both sides of equation (63) Taking the derivative, we get: (64) Combined equations (62) From equation (64), we can obtain: (65) Now let's define the substitution variable. , They are respectively: (66) (67) Substituting equations (63) and (66) into equation (55), we get: (68) Substituting equations (66) and (67) into equation (65), we get: (69) Substituting equations (68) and (69) into equation (58), we get: (70) Let's also define substitution variables. for: (71) Substituting equation (71) into equation (70), we get: (72) Among them, equation (72) is in Established at that time; And when At that time, according to equation (52) From equations (56) and (68), we can obtain: (73) Let substitution variables for: (74) By combining equations (73) and (74), we can obtain: (75) Substituting equation (75) into equation (72), we get: (76) Let substitution variables for: (77) Substituting equation (77) into equation (76), we get: (78) From equation (75), we can obtain: (79) Substituting equation (79) into equation (78), we get: (80) From equation (79), we can obtain: (81) Will time Recorded as Then, from equations (80) and (81), we can obtain and The function expression: (82) (83) From equation (41), we can obtain: (84) In the formula, , For the relevant constants of the rock under yield stress, based on multiple sets of yield stress state data and using equation (36), a least squares-based approach is adopted. The principle is obtained through curve fitting. Based on the aforementioned strength criterion, the obtained value can be obtained according to equation (36). and The function expression: (85) In the formula, , The relevant constants for rocks under peak stress are obtained by using curve fitting based on the least squares principle, according to multiple sets of peak stress data and using equation (85). For equation (41), let the substitution variables be respectively set. , for: (86) (87) On both sides of equation (41) Taking the derivative, we get: (88) Taking the logarithm of both sides of equation (86) yields: (89) Applying both sides of equation (89) simultaneously Taking the differential and using the conditions of equation (51), we can obtain: (90) Right now: (91) Applying both sides of equation (87) simultaneously Taking the differential and using the conditions of equation (51), we can obtain: (92) By combining equations (86), (87), (88), (91), and (92), we can obtain the MC nonlinear strength criterion. : (93) For the model parameters under the HB nonlinear strength criterion From equation (45), we can obtain: (94) In the formula, The values ​​represent the stress and strain corresponding to the peak points of the triaxial stress-strain curve of the rock; k and s are empirical parameters. set up: (95) (96) Accordingly, and For the rock to be in yield stress Empirical parameters at that time; Substituting equations (95) and (96) into equation (94), we get: (97) Substituting equations (95) and (96) into equation (43), we get: (98) Empirical parameters in the formula and The solution can be obtained by using multiple sets of yield stress state data and a curve fitting method based on the least squares principle. Peak stress It can be expressed according to equation (98): (99) In the formula, , For the rock at peak stress The empirical constant for the time can be obtained by using multiple sets of peak stress state data according to equation (99) and by adopting a curve fitting method based on the least squares principle; By combining equations (45), (95), and (96), we can obtain: (100) Set up substitution variables respectively , for: (101) (102) Applying equation (100) to both sides Taking the derivative, we get: (103) Taking the logarithm of both sides of equation (101) yields: (104) Applying both sides of equation (104) simultaneously Taking the differential and using the conditions of equation (51), we can obtain: (105) Right now: (106) Applying both sides of equation (102) simultaneously Taking the differential and using the conditions of equation (51), we can obtain: (107) By combining equations (100), (101), (102), (106), and (107), we can obtain the HB nonlinear strength criterion. : (108) The relationship between peak strain and confining pressure can be expressed as: (109) In the formula, for unknown parameters and The solution can be obtained by using multiple sets of peak stress state data and adopting a curve fitting method based on the least squares principle.

[0019] Step S4 verifies the effectiveness and rationality of the statistical constitutive model for damage in porous rocks under high ground stress, specifically including: Triaxial test data and curves of relevant rocks under different confining pressures in actual engineering are introduced. Based on this, the results of tests under different confining pressures are determined. Under these conditions, its strain The corresponding rock yield stress intensity is shown in Table 1.

[0020] Table 1 Rock yield strength parameters Based on equations (36) and (98), the rock yield strength index is obtained by curve fitting using Origin software based on the least squares method. It is 0.06144. The value was -54.3042, and the correlation coefficient of the fit reached 0.9708. It is 77.8317. The value was 5824.5747, and the correlation coefficient of the fit reached 0.9701. For example... Figure 2 and Figure 4 As shown.

[0021] Triaxial test data and curves of relevant rocks under different confining pressures in actual engineering are introduced. Based on this, the results of tests under different confining pressures are determined. Under these conditions, its strain The corresponding peak rock stress intensity is shown in Table 2.

[0022] Table 2 Rock peak strength parameters Based on equations (85) and (99), the rock yield strength index is obtained by curve fitting using Origin software, based on the principle of least squares. It is 0.0179. The correlation coefficient was 3.6402, and the fitted correlation coefficient reached 0.9983. It is 379.9768. The value was 5462.4706, and the correlation coefficient of the fit reached 0.9954. For example... Figure 3 and Figure 5 As shown.

[0023] According to equation (109), the least squares method is used, and curve fitting is performed using Origin software to obtain the result. It is 0.00248. The correlation coefficient of the fit reached 0.9698. For example... Figure 6 As shown in the figure.

[0024] Introducing triaxial test data and curves of relevant rocks under different confining pressures from actual engineering projects, and based on the test data and the theoretical expression in step S3, calculating the MC nonlinear strength criterion under different confining pressures. m , The elastic modulus of the rock in this experiment was determined using the method described in the aforementioned patent of this invention. 35.34 GPa, Poisson's ratio 0.25, setting The determination results for these parameters are listed in Table 3. 40.34 GPa.

[0025] Table 3 Constitutive model parameters under different confining pressures (MC nonlinear strength criterion) Substituting the above parameters into the model analysis and calculation provided in this invention patent yields the model's theoretical curve. The corresponding MC nonlinear strength criterion model theoretical curve and experimental curve are plotted in the same graph. Figures 7 to 11 As shown, the theoretical curves and experimental curves of the model in this invention match well, and their overall trends are similar, reflecting the nonlinear change process of the rock. In the stage before the yield stress point, the deviatoric stress of the theoretical curve is slightly smaller than that of the experimental curve. In the stage after the yield stress point, the experimental curve gradually flattens out, while the theoretical curve shows a downward trend. As the confining pressure increases, the rock undergoes strain hardening, and the theoretical curve tends to flatten out. This matches the actual situation well, thus verifying the rationality of the established constitutive model.

[0026] Calculate the results under different confining pressures under the HB nonlinear strength criterion. m , The elastic modulus of the rock in this experiment was determined using the method described in the aforementioned patent of this invention. 35.34 GPa, Poisson's ratio 0.25, setting The determination results for these parameters are listed in Table 4. 40.34 GPa.

[0027] Table 4 Constitutive model parameters under different confining pressures (HB nonlinear strength criterion) Substituting the above parameters into the model analysis and calculation provided by this invention patent yields the theoretical curve of the model. The theoretical curve of the HB nonlinear strength criterion model of this invention patent and the experimental curve are plotted in the same graph. Figures 12 to 16 As shown, the theoretical curves and experimental curves of the model in this invention match well and have similar overall trends, reflecting the nonlinear change process of the rock. In the stage before the yield stress point, the deviatoric stress of the theoretical curve is slightly smaller than that of the experimental curve. In the stage after the yield stress point, the experimental curve gradually flattens out, while the theoretical curve shows a downward trend. As the confining pressure increases, the rock undergoes strain hardening, and the theoretical curve tends to flatten out. This matches the actual situation well, thus verifying the rationality of the established constitutive model.

[0028] The theoretical curves of the HB nonlinear strength criterion model and the MC nonlinear strength criterion model of this invention are listed in the same graph as the experimental curves. Figures 17 to 21As shown, the two model curves in this invention patent can reflect the compaction stage, the elastic stage, the yielding stage, and the failure stage of rock material after the peak stress. In the compaction stage, the cracks between rock blocks are compressed, leading to an increase in the rock's elastic modulus (i.e., increased stiffness), resulting in a larger curve slope and a slightly downward convex trend. In the elastic stage, the rock's stress and strain satisfy the elastic model, and the curve slope represents the rock's elastic modulus. After the yield stress point, minor damage and plastic deformation occur inside the rock, weakening its resistance to deformation, thus reducing the curve slope and causing an upward convex trend. After the peak stress point, the internal structure of the rock is destroyed, and with continued pressure, macroscopic fracture surfaces appear, resulting in macroscopic block slippage, which causes a significant decreasing trend in the stress-strain curve. Moreover, under high confining pressures of 60 MPa and 70 MPa, the rock undergoes strain hardening, and the theoretical curve tends to flatten, which matches the actual situation well, thus verifying the rationality of the established constitutive model.

[0029] In step S5, considering the variation in initial porosity, a sensitivity analysis of the statistical constitutive model for damage in porous rocks under high in-situ stress is conducted, focusing on the influence of different initial porosities on the theoretical curve. This includes: To contain Taking 10 MPa as an example, five sets of initial porosity were set, and theoretical curves under the HB nonlinear strength criterion were plotted and compared. The percentages are 0%, 3%, 6%, 9%, and 12%, respectively.

[0030] Following the same solution order for the theoretical curve as described above, the model parameters are first obtained. and The elastic modulus of the rock in this experiment is 35.34 GPa, Poisson's ratio 0.25, from equation (48) we get E / (1- The results of determining these parameters are listed in Table 5.

[0031] Table 5. Parameter Determination Results Substituting the above parameters into the model analysis and calculation provided by this invention patent yields the theoretical curve of the model. The theoretical curves of the five initial porosity models under the HB nonlinear strength criterion of this invention patent are listed in the same curve graph, as shown in Figure 22.

[0032] from Figure 22 The initial porosity can be preliminarily determined. The following pattern emerges among the five theoretical curves for 0%, 3%, 6%, 9%, and 12% porosity: In the stage following the yield point, the greater the initial porosity and the smaller the deviatoric stress, the "lower" the theoretical curve appears. Combined with... Figure 22 This leads to the conclusion that in the stage after the yield point, the greater the initial porosity and the smaller the deviatoric stress, the "lower" the theoretical curve appears.

[0033] This invention provides a method for establishing a statistical constitutive model for damage in porous rocks under high ground stress. The theoretical curves of the model based on two nonlinear strength criteria are plotted and compared with corresponding experimental data curves to verify the effectiveness and rationality of the statistical constitutive model for damage in porous rocks under high ground stress. Furthermore, it analyzes that the deformation behavior of porous rocks under different confining pressures exhibits significant differences as the confining pressure increases: during the compaction stage, the pores between rock blocks are compressed, leading to an increase in the rock's elastic modulus, i.e., increased stiffness, resulting in a larger curve slope and a slightly downward convex trend. As the confining pressure gradually increases, the rock's strength increases accordingly, and the curve changes from a downward trend to a flattened trend after the peak point. This trend is consistent with actual engineering phenomena and provides strong support for understanding the deformation process of porous rocks. Finally, considering the change in initial porosity, the influence of different initial porosities on the theoretical curves of the model is examined, and a sensitivity analysis of the statistical constitutive model for damage in porous rocks under high ground stress is conducted.

[0034] The present invention also provides an apparatus for establishing a statistical constitutive model of high-stress porous rock damage for performing the aforementioned method, comprising: The porosity concept introduction module is used to introduce the concept of porosity and quantify the influence of pores on the volume change of porous rocks under pressure. The strength criterion construction module is used to construct a rock nonlinear strength criterion considering high ground stress by applying the MC nonlinear strength criterion and the HB nonlinear strength criterion, and to establish a rock micro-element strength measurement method that can reflect the nonlinear deformation characteristics of porous rocks. The damage statistical constitutive model establishment module is used to establish a damage statistical constitutive model applicable to the nonlinear deformation process of porous rocks under high geostress, and proposes a method for calculating the corresponding model parameters of the constitutive model. The verification module is used to plot theoretical curves based on the MC nonlinear strength criterion and the HB nonlinear strength criterion, and compare and analyze them with the corresponding experimental data curves to verify the effectiveness and rationality of the statistical constitutive model for damage to porous rocks under high ground stress. The sensitivity analysis module is used to consider the variation of initial porosity and conduct sensitivity analysis of the statistical constitutive model of damage in porous rocks under high ground stress, focusing on the influence of different initial porosities on the theoretical curve.

[0035] Specific examples have been used to illustrate the principles and implementation methods of this invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of this invention. Furthermore, those skilled in the art will recognize that, based on the ideas of this invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this invention.

Claims

1. A method for establishing a statistical constitutive model of damage in porous rocks under high ground stress, characterized in that, Includes the following steps: Step S1: Introduce the concept of porosity and quantify the influence of pores on the volume change of porous rocks under pressure. Step S2: Using the MC nonlinear strength criterion and the HB nonlinear strength criterion, construct a rock nonlinear strength criterion considering high ground stress, and establish a rock micro-element strength measurement method that can reflect the nonlinear deformation characteristics of porous rocks. Step S3: Establish a damage statistical constitutive model to simulate the nonlinear deformation process of porous rocks under high ground stress, and propose a method for calculating the model parameters corresponding to this constitutive model. Step S4: Plot the theoretical curves based on the MC nonlinear strength criterion and the HB nonlinear strength criterion, and compare and analyze them with the corresponding experimental data curves to verify the effectiveness and rationality of the statistical constitutive model for damage to porous rocks under high ground stress. Step S5: Considering the variation in initial porosity, conduct a sensitivity analysis of the statistical constitutive model for damage in porous rocks under high ground stress, focusing on the influence of different initial porosities on the theoretical curve.

2. The method according to claim 1, characterized in that, In step S1, the concept of porosity is introduced to quantify the impact of porosity changes on rock volume changes under pressure, specifically including: The porous rock mass is considered as three units: porous unit, damaged unit and undamaged unit; The stress on porous rocks is defined as apparent stress. The corresponding effective area is The effective areas of the damaged unit, the undamaged unit, and the porous unit are respectively... , , Then we have: （1） The stress experienced by an undamaged element is defined as the effective stress. Now, assuming only the undamaged elements are subjected to force, the stress on the entire rock and the stress on the undamaged elements have the following relationship: （2） Let the porosity of the rock be... According to the proportional relationship, we have: （3） The proportion of rock-damaged units is defined as the damage factor. According to the proportional relationship, we have: （4） Combined equations (1) Equation (4) yields a damage model characterizing porous rocks, expressed as follows: （5） Assuming the undamaged rock unit follows the generalized Hookean rule Then we have: （6） In the formula, and and The mechanical meanings of these two terms are the same, both representing effective stress. Deformation mode of undamaged units in rock ; Poisson's finite element in the rock ; This represents the microscopic strain of undamaged units within the rock. During rock deformation, there is a relationship of deformation coordination among the various rock elements. ,but: （7） In the formula, Indicates the apparent strain of the rock; Based on the above deformation compatibility relationships, then: （8） In the formula, Poisson's ratio for the entire rock; Combined equations (6) Equation (8) gives the effective stress as: （9） Substituting equation (9) into equation (5), we obtain the expression for apparent stress: （10） During the deformation process of porous rocks, the porosity changes continuously with the volume of the rock. Therefore, let the initial porosity of the rock be... Now, we take a tiny unit from the rock as the object of study, and denote its length as... , width is Gao Wei Assume that during the loading process, due to changes in pore volume, the length, width, and height of the representative element undergo compressive deformation, respectively. If we assume that the volume of the solid portion of the rock remains constant before and after deformation, then we can establish the following equation: （11） Furthermore, due to strain Then equation (11) becomes: （12） Rearranging equation (12) yields: （13） Since the strains are all small micro-quantities, cancel the right side of equation (13) , , and We can obtain: （14） For ease of writing, the following is hereby ordered: （15） Substituting equation (15) into equation (14) yields the porosity: （16） From equation (9), we can obtain: （17） （18） （19） From equation (5), we can obtain: （20） （21） Combined (17) From equation (29), we can obtain: （22） （23） Substituting equations (22) and (23) into equation (15) and then into equation (16), we get: （24）。 3. The method according to claim 2, characterized in that, In step S2, it is assumed that the strength of the rock element follows the Weibull distribution. Considering the influence of threshold damage, the following rock damage evolution model can be obtained: （25） In the formula, The strength of a rock micro-element; These are model parameters; Accordingly, the statistical constitutive model of damage in porous rocks can be expressed as: （26）。 4. The method according to claim 3, characterized in that, In step S2, taking the MC nonlinear criterion as an example, its corresponding intensity envelope function expression is: （27） In the formula, a and b are the calculation parameters corresponding to the function expression; Considering the geometric properties of the MC nonlinear criterion, we can obtain: （28） （29） Combined (28) Equation (29) gives: （30） From equation (27), we can obtain: （31） Substituting equation (31) into equation (30), we get: （32） By combining equations (27) and (32), we can obtain: （33） or: （34） Based on this combined with equation (28), we can obtain: （35） Therefore, for undamaged units in the rock, we have: （36） In the formula, , These are the calculation constants for the yield stress state; Accordingly, a method for measuring the intensity of infinitesimal elements can be established, namely: （37） Note that from equation (5), we can obtain: （38） （39） From equation (10), we can obtain: （40） Combined (37) Equation (40) gives the expression for the rock micro-element strength function based on the MC nonlinear strength criterion: （41）。 5. The method according to claim 4, characterized in that, In step S2, based on the fundamental principle of the HB nonlinear strength criterion, the stress expression can be obtained: （42） In the formula, It is the uniaxial compressive strength of rock k and s are empirical parameters; For undamaged units in the rock, we can obtain: （43） Accordingly, a method for measuring the strength of rock micro-elements can be established, namely: （44） Combined (38) Equations (40) and (44) give the expression for the rock micro-element strength function based on the HB nonlinear strength criterion: （45）。 6. The method according to claim 5, characterized in that, In step S3, when a complete, dense rock without obvious defects is taken and no confining pressure is applied, the rock micro-element strength is... Therefore, damage variable A value of 0 indicates that the rock has not been damaged. Assuming the damage variable D is zero, and the porous rock is subjected to a load P, let the initial porosity be... If the area subjected to the force is S, then: （46） （47） By combining (46) and (47), the elastic modulus of the undamaged element can be obtained. Overall elastic modulus of rock Quantitative relationship between them: （48） When the obtained rock is similar to that in the actual natural environment and has obvious defects, the proportion of pore units will be relatively large, and the influence of pore units cannot be ignored. In this case, a uniaxial compression test is performed, and the initially measured elastic modulus value is... Then, using the above-mentioned experimental results, The initial porosity can be obtained from the value of , according to equation (48). : （49） According to conventional triaxial tests, the initial state of the rock sample is under hydrostatic pressure. At this point, an initial axial strain is generated. The curve obtained from the experiment is a deviatoric stress curve. With axial strain The relationship curve; under hydrostatic pressure, the initial strain can be obtained by combining equations (10) and (24). : （50） Now assume that the coordinates of the peak point of the conventional triaxial test curve for porous rocks are... We can obtain: （51） In the formula, Represents the differential symbol; From equation (10), we can obtain: （52） According to equation (24), we can obtain: （53） Introduction , , As a substitute variable, we have: （54） （55） （56） Based on equations (54), (55), and (56), equation (53) can be transformed into the following expression: （57） By combining equations (51), (52), (54), and (57), we can obtain: （58） On both sides of equation (56) Taking the derivative, we get: （59） Taking the logarithm of both sides of equation (55) yields: （60） Then, adjust both sides of equation (60) Taking the derivative, we get: （61） Combining equation (55) and equation (61), we get: （62） From equation (25), we can obtain: （63） On both sides of equation (63) Taking the derivative, we get: （64） Combined equations (62) From equation (64), we can obtain: （65） Now let's define the substitution variable. , They are respectively: （66） （67） Substituting equations (63) and (66) into equation (55), we get: （68） Substituting equations (66) and (67) into equation (65), we get: （69） Substituting equations (68) and (69) into equation (58), we get: （70） Let's also define substitution variables. for: （71） Substituting equation (71) into equation (70), we get: （72） Among them, equation (72) is in Established at that time; And when At that time, according to equation (52) From equations (56) and (68), we can obtain: （73） Let substitution variables for: （74） By combining equations (73) and (74), we can obtain: （75） Substituting equation (75) into equation (72), we get: （76） Let substitution variables for: （77） Substituting equation (77) into equation (76), we get: （78） From equation (75), we can obtain: （79） Substituting equation (79) into equation (78), we get: （80） From equation (79), we can obtain: （81） Will time Recorded as Then, from equations (80) and (81), we can obtain and The function expression: （82） （83） From equation (41), we can obtain: （84） In the formula, , For the relevant constants of the rock under yield stress, based on multiple sets of yield stress state data and using equation (36), a least squares-based approach is adopted. The principle is obtained through curve fitting. Based on the aforementioned strength criterion, the obtained value can be obtained according to equation (36). and The function expression: （85） In the formula, , The relevant constants for rocks under peak stress are obtained by using curve fitting based on the least squares principle, according to multiple sets of peak stress state data and using equation (85). For equation (41), let the substitution variables be respectively set. , for: （86） （87） On both sides of equation (41) Taking the derivative, we get: （88） Taking the logarithm of both sides of equation (86) yields: （89） Applying both sides of equation (89) simultaneously Taking the differential and using the conditions of equation (51), we can obtain: （90） Right now: （91） Applying both sides of equation (87) simultaneously Taking the differential and using the conditions of equation (51), we can obtain: （92） By combining equations (86), (87), (88), (91), and (92), we can obtain the MC nonlinear strength criterion. : （93） For the model parameters under the HB nonlinear strength criterion From equation (45), we can obtain: （94） In the formula, The values ​​represent the stress and strain corresponding to the peak points of the triaxial stress-strain curve of the rock; k and s are empirical parameters. set up: （95） （96） Accordingly, and For the rock to be in yield stress Empirical parameters at that time; Substituting equations (95) and (96) into equation (94), we get: （97） Substituting equations (95) and (96) into equation (43), we get: （98） Empirical parameters in the formula and The solution can be obtained by using multiple sets of yield stress state data and a curve fitting method based on the least squares principle. Peak stress It can be expressed according to equation (98): （99） In the formula, , For the rock at peak stress The empirical constant for the time can be obtained by using multiple sets of peak stress state data according to equation (99) and by adopting a curve fitting method based on the least squares principle; By combining equations (45), (95), and (96), we can obtain: （100） Set up substitution variables respectively , for: （101） （102） Applying equation (100) to both sides Taking the derivative, we get: （103） Taking the logarithm of both sides of equation (101) yields: （104） Applying both sides of equation (104) simultaneously Taking the differential and using the conditions of equation (51), we can obtain: （105） Right now: （106） Applying both sides of equation (102) simultaneously Taking the differential and using the conditions of equation (51), we can obtain: （107） By combining equations (100), (101), (102), (106), and (107), we can obtain the HB nonlinear strength criterion. : （108） The relationship between peak strain and confining pressure can be expressed as: （109） In the formula, for unknown parameters and The solution can be obtained by using multiple sets of peak stress state data and adopting a curve fitting method based on the least squares principle.

7. The method according to claim 6, characterized in that, Step S4 verifies the effectiveness and rationality of the statistical constitutive model for damage in porous rocks under high ground stress, specifically including: Based on the experimental data and curves, and according to the above theoretical formulas, the parameter values ​​under different confining pressure conditions are calculated. The theoretical curves of the damage statistical constitutive model are obtained based on the parameter values, and compared with the corresponding experimental data curves. The calculated model parameter values ​​are then analyzed.

8. The method according to claim 7, characterized in that, In step S5, considering the variation in initial porosity, a sensitivity analysis of the statistical constitutive model for damage in porous rocks under high in-situ stress is conducted, focusing on the influence of different initial porosities on the theoretical curve. This includes: Under certain confining pressure conditions, five sets of different initial porosity were set to plot theoretical curves and conduct comparative analysis. The five initial porosities were set to 0%, 3%, 6%, 9%, and 12%, respectively.

9. A device for establishing a statistical constitutive model for high-stress porous rock damage, used to execute the method for establishing a statistical constitutive model for high-stress porous rock damage according to any one of claims 1-8, characterized in that, include: The porosity concept introduction module is used to introduce the concept of porosity and quantify the influence of pores on the volume change of porous rocks under pressure. The strength criterion construction module is used to construct a rock nonlinear strength criterion considering high ground stress by applying the MC nonlinear strength criterion and the HB nonlinear strength criterion, and to establish a rock micro-element strength measurement method that can reflect the nonlinear deformation characteristics of porous rocks. The damage statistical constitutive model establishment module is used to establish a damage statistical constitutive model applicable to the nonlinear deformation process of porous rocks under high geostress, and proposes a method for calculating the corresponding model parameters of the constitutive model. The verification module is used to plot theoretical curves based on the MC nonlinear strength criterion and the HB nonlinear strength criterion, and compare and analyze them with the corresponding experimental data curves to verify the effectiveness and rationality of the statistical constitutive model for damage to porous rocks under high ground stress. The sensitivity analysis module is used to consider the variation of initial porosity and conduct sensitivity analysis of the statistical constitutive model of damage in porous rocks under high ground stress, focusing on the influence of different initial porosities on the theoretical curve.

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